Graph mining in bioinformatics

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Graph mining in bioinformatics

• Laur Tooming

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Graphs in biology

• Graphs are often used in bioinformatics for
  describing processes in the cell
• Vertices are genes or proteins
• The meaning of an edge depends on the type of the
  graph
• Protein-protein interaction
• Gene regulation

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What were looking for

• We want to find sets of genes that have a
  biological meaning.
• Idea find graph-theoretically relevant sets of
  vertices and find out if they are also
  biologically meaningful.
• Simple example connected components
• A more advanced idea graph clustering. Find
  subgraphs that have a high edge density.

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Markov Cluster Algorithm (MCL)

• If there is cluster structure in a graph, random
  walks tend to remain in a cluster for a long time
• Graph modelled as a stochastic matrix sum of
  entries in a column is 1
• aij - probability that randomly walking out of j
  will go to i on the next step
• Bigger edge weight means greater probability of
  choosing that edge

• Stijn van Dongen, Graph Clustering by Flow
  Simulation. PhD thesis, University of Utrecht,
  May 2000.
• http//micans.org/mcl/

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Markov Cluster Algorithm (MCL)

• Two procedures, inflation and expansion, are
  applied alternatively
• Expansion matrix squaring
• considers longer random walks
• Inflation raising entries to some power,
  rescaling to remain stochastic
• Weakens weak edges and strengthens strong ones
• Converges to a steady state

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Markov Cluster Algorithm (MCL)

• Images from http//micans.org/mcl/ani/mcl-animatio
  n.html

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Betweenness centrality clustering

• An edge between different clusters is on many
  shortest paths from one cluster to another.
• An edge inside a cluster is on less shortest
  paths, because there are more alternative paths
  inside a cluster.
• Betweenness centrality of an edge - the number of
  shortest paths in the graph containing that edge.
• Remove edges with the highest centrality from the
  graph to obtain clustering.
• Optimisations
• instead of all shortest paths, pick a sample of
  vertices and calculate shortest paths from them
• remove several edges at once

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GraphWeb

• Web interface for analysing biological graphs
• Simple syntax for entering graphs
• multiple datasets
• directed edges
• edge weights
• Visualising graphs with GraphViz
• Finding biological meaning with gProfiler
• ds1 A gt B 10
• ds2 A gt B 4
• ds1 B C 5
• ds2 C gt D 12

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Combining several datasets

• Whether or not there is an edge between two
  vertices is determined in biological experiments,
  which may sometimes give false results.
• For a given graph different sources may give
  different information. Some sources may be more
  trustworthy than others.
• We would like to combine different sources and
  assess the trustworthyness of each edge in the
  resulting graph.
• Edge weight in summary graph sum over datasets
• w(e,G) S w(e,Gi)w(Gi)

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Combining several datasets
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The end